Chapter 2 - Models of Dynamic Processes and Signals

Abstract

Process identification is the construction of models from measured data for certain utilitarian purposes. The first step in the total-identification procedure is to determine a class of models in which the most suitable model is to be sought. This chapter reviews some well-known results on the way to describe dynamic processes and signals using linear models and block-oriented nonlinear models. Linear models form the most important and well-developed class of models, both in practice and in theory. Although linear models represent idealized processes in the real world, the approximations involved are often justified for the given applications of the models. A typical example is to describe the behavior of an industrial process, possibly nonlinear, by a linear time-invariant model around a working point. The chapter also discusses continuous-time models, discrete-time models, and models of multi-input multi-output (MIMO) processes. Most of the real-world systems have nonlinear behavior and linear models are only approximations for a small range of process operation. To extend the validity of models and the applicability of model-based control, some nonlinearity needs to be included in the model set. The difficulty in working with nonlinear models is the lack of a unified theoretical representation of various nonlinear behaviors. The chapter describes nonlinear representations of dynamic processes and some simple nonlinear models that are suitable for parametric identification schemes.